(auteur) In this paper, a robust unscented Kalman filter (UKF) based on the generalized maximum likelihood estimation (M-estimation) is proposed to improve the robustness of the integrated navigation system of Global Navigation Satellite System and Inertial Measurement Unit. The UKF is a variation of Kalman filter by which the Jacobian matrix calculation in a nonlinear system state model is not necessary. The proposed robust M–M unscented Kalman filter (RMUKF) applies the M-estimation principle to both functional model errors and measurement errors. Hence, this robust filter attenuates the influences of disturbances in the dynamic model and of measurement outliers without linearizing the nonlinear state space model. In addition, an equivalent weight matrix, composed of the bi-factor shrink elements, is proposed in order to keep the original correlation coefficients of the predicted state unchanged. Furthermore, a nonlinear error model is used as the dynamic equation to verify the performance of the proposed RMUKF with a simulation and field test. Compared with the conventional UKF, the impacts of measurement outliers and system disturbances on the state estimation are both controlled by RMUKF.

(auteur) Fault detection and identification (FDI) in either a stand-alone GPS or in integrated GPS/INS systems is essential for improving the quality of positioning, navigation, and many other applications. The assumption that the observations include a single fault has been considered intensively in literature. However, this assumption may not necessarily be valid due to the fact that multiple faults may exist simultaneously. In this study, separability of multiple faults in GPS/INS integration systems has been analysed geometrically and statistically. This has been achieved through testing how large correlation coefficient between any pair of fault tests statistics increases the probability of faults misidentification. In addition, a new calculation procedure of correlation coefficient when four faults appear in the observations has been developed. This procedure considers calculation the correlation between a single and a punch of measurements combined together. The results show that there is a strong relationship between the value of correlation coefficient and the probability of misidentification. Furthermore, a significant relationship between the correlation and the fault test values can be found when splitting the measurements combinations into groups based on the combination similarity. Nevertheless, this relationship can be defined without splitting the measurements into groups when using a new correlation procedure for four faults case. The geometric representation shows that large correlation coefficient reflects small angle between the correlation and the x-axis; whereas the angle between the fault-test vectors and the x-axis becomes wider when a tiny correlation exist.

(auteur) Key message : We compared two methods for detailed individual tree measurements: single image photogrammetry (SIP), a simplified, low-cost method, and the state-of-the-art terrestrial laser scanning (TLS). Our results provide evidence that SIP can be successfully applied to obtain accurate tree architectural traits in mature forests.
Context : Tree crown variables are necessary in forest modelling; however, they are time consuming to measure directly, and they are measured in many different ways. We compare two methods to obtain crown variables: laser-based and image-based. TLS is an advanced technology for three-dimensional data acquisition; SIP is a simplified, low-cost method.
Aims : To elucidate differences between the methods, and validate SIP accuracy and usefulness for forest research, we investigated if (1) SIP and TLS measurements are in agreement in terms of the most widely used tree characteristics; (2) differences between the SIP traits and their TLS counterparts are constant throughout tree density and species composition; (3) tree architectural traits obtained with SIP explain differences in laser-based crown projection area (CPA), under different forest densities and stand compositions; and (4) CPA modelled with SIP variables is more accurate than CPA obtained with stem diameter-based allometric models. We also examined the correspondence between local tree densities extracted from images and from field measurements.
Methods : We compared TLS and SIP in a temperate pure sessile oak and mixed with Scots pine stands, in the Orléans Forest, France. Standard major axis regression was used to establish relations between laser-based and image-based tree height and diameter at breast height. Four SIP-derived traits were compared between the levels of stand density and species composition with a t test, in terms of deviations and biases to their TLS counterparts. We created a set of linear and linear mixed models (LMMs) of CPATLS, with SIP variables. Both laser-based and image-based stem diameters were used to estimate CPA with the published allometric equations; the results were then compared with the best predictive LMM, in terms of similarity with CPATLS measurement. Local tree density extracted from images was compared with field measurements in terms of basic statistics and correlation.
Results : Tree height and diameter at breast height were reliably represented by SIP (Pearson correlation coefficients r = 0.92 and 0.97, respectively). SIP measurements were affected by the stand composition factor; tree height attained higher mean absolute deviation (1.09 m) in mixed stands, compared to TLS, than in pure stands (0.66 m); crown width was more negatively biased in mixed stands (− 0.79 m), than in pure stands (− 0.05 m); and diameter at breast height and crown asymmetry were found unaffected. Crown width and mean branch angle were key SIP explanatory variables to predict CPATLS. The model was approximately 2-fold more accurate than the CPA allometric estimations with both laser-based and image-based stem diameters. SIP-derived local tree density was similar to the field-measured density in terms of mean and standard deviation (9.6 (3.5) and 9.4 (3.6) trees per plot, respectively); the correlation between both density measures was significantly positive (r = 0.76).
Conclusion : SIP-derived variables, such as crown width, mean branch angle, branch thickness, and crown asymmetry, were useful to explain tree architectural differences under different densities and stand compositions and may be implemented in many forest research applications. SIP may also provide a coarse measure of local competition, in terms of number of neighbouring trees. Our study provides the first test in mature forest stands, for SIP compared with TLS.

(auteur) Leveling is a traditional geodetic surveying technique that has been used to realize a vertical datum. However, this technique is time consuming and prone to accumulate errors, where it relies on starting from one station with a known orthometric height. Establishing orthometric heights using Global Navigation Satellite Systems (GNSS) and a geoid model has been suggested [14], but this approach may involve less precisions than the direct measurements from leveling. In this study, an experimental study is presented to adjust the highly accurate leveling observations along with orthometric heights derived from GNSS observations and a geoid model. For the geoid model, the National Geodetic Survey’s gravimetric geoid model (TxGEOID16B) and hybrid geoid model (GEOID12B) were applied. Uncertainties in the leveled height differences, GNSS derived heights, and the geoid models were modeled, and a combined adjustment was implemented to construct the optimal combination of orthometric, ellipsoidal, and geoid height at each mark. As a result, the discrepancy from the published orthometric heights and the CSM (Corrector Surface Model) based adjusted orthometric heights with GEOID12B showed a mean and RMS of -8.5 mm and 16.6 mm, respectively, while TxGEOID16B had a mean and RMS of 28.9 mm and 34.6 mm, respectively. It should be emphasized that this approach was not influenced by the geodetic distribution of the stations where the correlation coefficients between the distance from the center of the surveying network and the discrepancy from the published heights using TxGEOID16B and GEOID12B are 0.03 and 0.36, respectively.